Torsion-resisting rail



Oct. 21, 1941.' G. R. BURKHARDT TORsIoN-REsIsTING RAIL Filed April 1o, 1940 l 1 1 1 l l )x l l l X i FIGS 3 sheets-sheet 2 ABOUT HORIZ. N.A. WTA lER YARD -|29.7 LBS, I30. 8 LBS.

AREA or clRcLE mscmso 1N MEAD or RAIL 3.33 1112A HEAD oF RA1L 4.44111? RAT|o=AREA oF clRcLE To AREA oF HEAD= 0.75

G. R. BURKHARDT TORSION-RESISTING RAIL Filed April 10, 1940 5 Sheets-Sheet 3 Patented Oct. 21, 1941 aan sur TRSION-RESHSTNG Rm George R. Burkhardt, Chicago, lill'. A Application April lil, 1940, Serial No. 328,971

(ci. ass-125) I 13 Claims.

This invention relates to railway rail and particularly to a torsion-resisting rail involving certain physical and dimensional changes and a novelldistribution of metal, and having for its principal object a practical solution of overcoming undesirable and dangerous conditions in railway track due to torsional strains, as well as to eccentric loading conditions and impacts.

The tendency of American rail design has been in the direction of increasing vertical rail stiffness resulting in the making oi.' a thin high section, and experience has shown that the rapid change in cross-section of the conventional rail has resulted in very high stresses, concentrating in the llets joining the head and web, and it is one of the important objects of the present invention to provide a novel metal distribution which will equalize the stresses at all points and at the same time obtain a greater torsional and exural rigidity. More specifically other Vdenite objects of the invention are to improve the torsional rigidity of the head to give greater resistance to web roll, to relieve peak stresses by inl creased thickness of the top of the web; reinforcing or ribbing the web, not only for strengthening purposes but also improving the texture of metal; increasing the inertia moment of the whole rail .and improving the point or position of loading.

It has been found that most rails measured in track have been subjected to large lateral loads, as well as eccentrically applied vertical loads, and maximum stresses have been found concentrated in the llet under the head. The combination of these lateral and eccentric vertical loads operate to twist and bend the rail, and according to the present invention a new construction is provided for a rail which results in a uniform distribution of stresses and in the bringing of the wheel load nearer the center of the rail, `with a consequent reduction in peak stresses in the llet under the rail head. It is therefore the purpose and object of the present invention to provide a novel distribution of metal which will distribute the stress equally, thereby overcoming the weakness of entirely eliminate, the counterbalance kinks found in present comparable rail in track, as well as reducing transverse fissures, resulting from growth of fatigue cracks, -by reason oi the fact that the new rail is sd designed as to relieve torsional and exural stress.

With these and other objects in view which will readily appear to those familiar with the art,v as the details of the invention are better understood, the same consists in the novel construction and features hereinafter described and illustrated in the drawings, in which:

Figure 1 is a cross-sectional view of the new torsion-resisting rail illustrating the theory upon which the s ame is designed and the metal distribution therein; this'view illustrates the new rail structure superimposed over a comparable Standard A.R. E. A. 131 lb. rail and showing a maximum depth of rail head in which the iishing surfaces at the underside of the rail head are disposed a. distance below the corresponding iishlng surfaces of the comparable rail. However, the bar for this rail is fully as stii as the bar for the A. R. E. A. rail since the greater depth of the present rail head permits a deep joint bar section as shown in dotted lines.

Figure 2 is asimilar view, -on the section line 2-2 of Figure 3, showing a practical form'. of the invention embodied in a 130 1b. rail and compresent comparable rails under the head and in 4 the head itself.

to excess loadingresulting from the dynamic` .augment of the counterbalancel of locomotive drivers, as well as eccentric loading conditions and impacts; the new metal distribution involved pared with the A.. R. E. A. 131 lb. rail shown in dotted lines; this rail has the major portion of the area of the head equal to that of the largest circle that can be inscribed in the head, also the desired position of the center of twist; and the height of the fishing space is substantially that of the height of the comparable A. R. E. A. 131 lb. rail, permitting the use of existing bars for 131 lb. rail; the'said figure of the drawings having 'placed thereon the designations, in inches and fractions of inches, giving the permissible dimensions of the various parts of the rail and their new and novel proportionate relations to each other in accordance with the mathematical demonstrations herein.

Figure 3 is a detail fragmentary plan view inin the new rail serving to greatly reduce, if not ance with the illustration ofthe following Fig. 6.

` web Figure'is'aviewsimilartolilgcomparinga 131 ib. rail of the new invention with a- 131 lb.

A. R. E. A. rail and showing the fishing height of the two rails approximately the same, thereby .permitting the use of existing joint bars for 131 l lb.'rail.

Like references designate corresponding in the `several figures of the drawings.

M shown in the drawingsthe new rail includes the head H of pentagonal shape, the web W and the base B, the latter being inclusive of the usuall base flanges b, and F and F'. designate respectively the fillet connecting the head with the and the llet connecting the web with the base.

'I'he metal distribution of the new rail involves certain structural characteristics involving a rad- 131 lb. rail. This Standard type rail is representative of most Standard rails now in use in the particularthat its head has oppositely extending' flanges of unnecessary width and which in practice have proven to be responsible for split rail heads due to thev eccentric loading thereof, and always the total width of the head of this Standard rail is materially greater than the diameter" of the largest circle that can be inscribed within the head, and the ratio of the area of the v,circle to the cross sectional area of the head is 'less than 65% whereas, according to the present invention, the width of .the head of the new. rail may be equal tothe diameter of a circle so in- .scribed and the ratio of area of circle to the cross-sectional area of head is substantially '15% or more. v

A fundamental phase of the metal distribution in the head of vthe new rail is determined from Standard rail, which for purposes of comparison .is shown in the drawings to be the A. R. E. A.

tangent to the sides of the head and the fillets F,

and with reference to the total width of the new rail head structure of the present invention it will be understood that a fractional mill tolerance must necessarily be allowed on either side of the circle, as for instance, plus or minus, or a total of 5/8" plus or minus.- In connection with this total depth of the new rail head structure an important considerationl of the invention lsto provide the maximum ratio of the depth of the head to its width, as shown in Fig. l and a minimum ratio of its depth to its width, as shown in Figs. 2 and 6, as well as to provide for maintaining approximately the ratio` of the width of the web to the width of the head as in the preferred ratios shown in Figs. 2 and 6 of the drawings. It should also be noted that the new 'metal distribution of the presentrail provides for I an inertia'moment of the head about its symmetry axis which is greater than about its horizontai line of centroids since the width of the head is greater than its depth.

Another feature of practical importance in the new rail of the present invention is to providea metal distribution resulting in a predeter-v l mined position of the center of twist of the rail the well known predicate that for two sections having the same area, thel section more nearly cylindrical or circular has the greater torsional stiifness, and that outstanding changes and excessive` widths, as found in present rail sections,

` have little `or no improving eilect as to that stilening'. function.` Therefore, the metal distribution in the head of the new rail is computed from the ideal cross-sectional shape most resistant to torsional stresses, that is, from a cylindrical cross-sectional shape, which is represented i ,in the present disclosure by what is termed as an inscribed uniformstress circle" designated by the numeral I in the drawings and corresponding ,to the ideal cylindrical shape. With reference to this uniform stress.circle it will be noted that the new head structure preferably has a width approximately equal to the diameter of the inscribed circle betweenthe 'top of the head and the fillets F Joining the head and webof the rail. From this it will be seen that forv two rails having the same area, the same web and the lsame base, the rail is stifiest when the area4 of the inscribed circle approximately equals the l major portion ofthe cross-sectional area of the section. The location of this center of twist is an important factor contributing to the torsion-resisting capacity of the new rail, and therefore the location of the center of twist ofthe new rail is correlated to the new metal distribution in the head and vbottom llet portions of the rail. In most forms of the invention this center of twist, as Shown, is nearest to the stilfest flange and its elevation is at or below the elevation .of the point of intersectiony or compounding of the web curve and the llet curve which joins the web and the base.

In proportional relation to thehead structure and the web structure the present invention inhead. In the illustration of Fig. 1, representing i the lbasic phase of the present invention, it will be seen that only 'relatively' small poxticnsof f metal, ,of comparatively'little stress value are leftoutside of the inscribed stress circle. It will 1 bel apparent from Figures 2 and 6 that the pril mary basis 'of the new metal distribution is prolvolves na widening or thickening of the head and base llets F-and F' as compared with the thickness of those llets in the comparable Standard rail and in its preferable embodiment the invention also includes, at and within the head llets,

projecting fillet stiifening ribs 2 struck on a radius length of the rail. Corresponding web and base iillet stiiening ribs I are formed at opposite sides Aof' the web of therail and extend into and'over the base illlets F', said stiffening ribs 3 preferably extending upward fromthe base fillets to a point approximately at the neutral axis of the new rail and being in *alternated or staggered relation upon opposite sides of the rail thereby maintaining uniformity of `section of the rail throughout.-

Taking ,intoconsideration the physical and dimensional changes involved in the new rail' structure over that of the comparable Standard rail it will be seen from the physical properties ofl these comparable rails, appearing on the drawings -for convenient reference, that for approximately trapezoidal sections. If the ends were made disthe same area of head, web, base and approximately the same weight, the new torsion-resisting rail, of the present inventionl has a substantially increased moment of inertia over that of the corresponding Standard rail, two comparisons being shown respectively in Figs. 2 and 6. In the comparison of physical properties shown in Fig. 2 of the drawings there is illustrated in this drawing the new rail of a 130 lb. superimposed over and compared with the 131 lb. A. R. E. A. rail, showing the new metal distribution to 'provide a definite increase of the moment of inertia over that of said v'comparable Standard rail in addition to the uniform stress distribution avoiding concentration of stresses in the head fillets of the rail; andin Fig. 6 the .properties given show that for 131 lb."torsionresisting rail according to the present invention compared with the same weight Standard rail the increased moment of inertia is been lightened considerably. In short, the gen-v eral result of the metal distribution of the present torsion-resisting rail is to equalize the stresses at all points, and at the same time obtain a greater torsional and flexural rigidity, and the basis of the new metal distribution accomplishing these highly desirable results is mathematically demonstrable according to the succeeding explanation of the theory underlying the invention:

The torsional resisting moment of a rail section is a function of the torsional constant K; 6, the angle of twist in radians per inch and the shearing modulus of elasticity G, and equals the product K G 9.

The torsional constant is a measure of the torsional rigidity and twisting deflections. For a circular section, K equals the polar moment of in. ertia and is less for non-circular sections such as the rail.

The torsional constant of a rail or I beam is the sm of the constants of the iianges ,(head and base), the constant of the connection of web and flanges and of the web, and the torsional constant of the head of the rail may Ibe shown to vary as the third power ot the thickness o! the head and that increasing the width of the head has small effect.

Saint Venant has shown that the constant for a rectangle of depth n and width C is where Vis a factor depending on the ratio and may be derived by test. The expression continuous, one might state i n30 Kmsvery nearly,` and for any dierential width da:-

along the section usda: l K=T be two trapezoids anda rectangular part. Let the thickness at any point on the trapezoids be taken --2Vn4 represents a term known in studies of torsion as the end or corner loss.' For sections such as the rectangle, the area at the ends have little or no resistance to torsion. 'From stress evaluation by Prandtls methodv of. membrane analogy the end loss is shown by the sloping down ot the membrane or soap lm to meet the edges of the short dimensions of. rectangular or as il and C the Width. Then if the ends are assumed discontinuous 1 C' K- o gdx The total slope of either of the trapezoids is very nearly ml-'7L from which y may be expressed in terms of and n, and the integral becomes From this the end s should be deductedand the constant becomes Considering the head of the rail as the sum of two trapezoids and a rectangle of width T and depth M1, and if the effect of the corner curves are omitted, the torsion constant of the head isapproximately The torsion'constant KH of the head as shown' in Fig. 1 may be more closely determined by mechanical integration or by the well known method of thin strips of width da: and depth y obtained by scaling andthe formula The torsion constant ofthe web of an I section or web of rail of uniform thickness T1 is readily obtained from Saint Venants formulaby considering the web as a discontinuous section between the flanges, giving equals the diameter of the inscribed circle and radius of llet (R) thickness of ange (Mh The values of a for structural beams have been .obtained by G. W. Trayer and H. W. March, Ad-

visory Committee for Aeronautics report No. 334 and appear in structural hand books, and other the equations:

authorities upon which the foregoing mathematical formulae are based are:

Inge Lyse, Mem. A. S. C. E. and B. G. Johnston,-

Jun. A. S. C. E.'on Torsion in Structural Beams.

Raymond J. Roarks Formulas for Stresses and Strains. v

Timoshenkos Strength of Mate Seelys Advanced Mechanics of'Materials.

Since, as stated, the torsion constant Ka of the whole rail is the sum of the constants derived above, it is readily seen that the rigidity of the rail is most eiiiciently obtained by incorporating the major portion of the area of the head inthe circle inscribed between top of the rail and illlets at the juncture of web and head and tangent .to the sides of the head as shown in Fig. 1. In torsion tests it was found that a very slight variation in the diameter of the inscribed circle effected rapid change in the stresses.

Ithas been pointed out that the result of the broad or excessivelywide head of the comparable Standard "r-rail brings about an early flow of the metal in the head toward the outside and also involves a high percenatge of split heads due to the concentration of the stresses in the head fillets of the rails, so one of the important objects of the present invention, as stated, is to provide the ultimate in a high moment-minimum of inscribed circle equals the major portion-of the gravity of the head above the center of the circle inscribed between the sides of the head and tangent to the llets joining the head and web.

In connection with the foregoing importance' A must be vgiven to locating the center of twist of the rail 'and this is denltely determied from 'IH-Is Lalxi-z nana Ie respectively denetefthe moments or niin the ratio of.4:1 to the horizontal, and it is also l.

of'practical importance in carrying forward the invention to have the side faces of the rail head I Fromthe foregoing it is thought that the essential features of the invention will be understood without further description, and changes or modifications within the scope of the appended claims may be resorted to without departing from v the spirit or sacrificing .any of the advantages of the invention.

I claim:

1. A railcomprising abase.- web and head, prof 3. A rail comprising a base, web and head and provided upon opposite sides' with projecting.'

stiiening ribs extending downward from a point appronimately at the neutral axis of the rail toapoint within the base fillets and alternately arranged upon opposite sides of the rail thereby to maintain uniformity of cross-section of the rail throughout within the area of the said ribs,

4. A rail comprising a base, web and head having the major portion of the cross-sectional area -of the head within an inscribed circle Atangent to the top and to the fillets joining the head and the web, and providedin both the head and web iillets with projecting stiftening ribs arranged in staggered relation upon opposite sides of the rail 4 thereby to maintain uniformity of cross-secertia of the head and base sections vwith respect to the axis ofV symmetry ofthe rail sections. L equals distance between line of centroids of head and base. La equals distance from 'line of centroids of base to center of twist. L1 equals dis'- tance between line of centroids of head to center of twist. 'I'he center of twist is nearest to the stiilest flange. and the new metal distribution I locates this center in the thickest-part of the web, that is, the elevation of this center of twist in the new torsion-resisting rail is usually at or below the elevation of the point of compounding of the web curve and the fillet curve joining'web i and base.

As to the dimensional phase of the new. rail vthat is importanty in the further particular that the iilshing angle of the new rail is approximately the range .of 13 or 15". and thatthe rail is so proportioned'that its height is greater than the width-ofthe base and that the width of the observed4 from theillustrations that the planes tional area throughout.

5. A rail inclusive of a head in which the area of an inscribed circle therein is-at least 75% of the entire cross-sectional areathereof. the said rail being further provided'at andl within `the head llets with projecting fillet stiifening ribs and arranged to maintain a uniform cross-sec- I tional thickness of the head llet neck through. out the length of the m11;

6; A rail inclusive of a head in which the area f and arranged'to maintain a uniform cross-sectional thickness of the base fillet neckv throughout the length'of the rail.

'1. A railway rail comprisinga pentagonalshaped head, 'a web, a pentagonal-shaped base,

head-web fillets at the junction of said head with said web and base-web fillets at the junction of said web and base forming a 13 to 15 fishing angle, the width of said head being greater than its depth and within one-and-three-eighths times its depth and less than one-half the width of said base, the width of said base being less than the height of the rail, the radii vof said head-web-iillets being not less than one-half vthe minimum thickness of said web, and the mini-"- mum thickness of said web being not les's than one-fourth the width of said* head so that the of the .width of'said head.

v oftheunderside of the'headarepreferably sloped 7a. '8. A railway rail*v comprising a pentago'nai'- shaped head, a web, 'a pentagonal-shaped base, head-web fillets at the junction of said head with said web and base-web fillets at the Junction of said web and base forming a 13 to 15 fishing, the width of said head being greater than its depth and within one-and-three-eighths times its depth and less than one-half the width of said base, thewidth of said base being less than the height of the rail, the radii of said head-web fillets being not less than one-half the minimum thickness of said web, 'and lthe minimum thickness of said web being not less than one-fourth the width of said head so that the torsional constant of said head plus end loss is not less than one-tenth times the fourth power of the width of said head; the area of a circle inscribed in said head tangent to the head-web fillets and to the top -of the head being equal to at least 75% of the area of the head. Y

9. A railway -rail comprising a pentagonalshaped head, a web, a pentagonal-shaped base, base-web'fillets at the junction of saidbase with said web and head-web fillets at the junction of said web and head-web llets at thejunction of said head with said web, said rail having a proportional distribution of metal throughout characterized by having at least 75% of the area of its head within a circle inscribed in the head tangent tothe head web fillets and to ther top of the rail, and having the minimum web thickness of at least one-fourth the head width and not more than twice` the radii of the head-webA fillets to provide, as' compared, e. g., with a Standard A. R. E. .A. -T-rail of approximately equal weight, an increased moment of inertia.. diminished area for the head, a torsional c'onstant (Kn) for the head of greater torsion resisting capacity thanl that of said comparable A. R.. E. A. Standard T-rail, and a torsional constant (Kr) for the head-web fillets at least 25% greater than the torsional constant of the head-web fillets of the said comparable T-rail.

12. A railway rail comprising a head, a web, a base, head-web iillets at the junction of said head with said web, and base-web fillets at thel junction of said base with said web, said rail having a proportional `distribution of metal throughout characterized by having the major portion of the area of its head within a circle inscribed in the head tangent to the head web less than one-half the width of said base, and

said base having a width less than the height of the rail, whereby the torsional constant of the head plus end loss is at least one-tenth times the fourth power of the width of said head and the center of twist of the rail is located below the points of compounding of the base-web fillets with the web.

10. A rail comprising a pentagonal-shaped head, a web, a pentagonal-shaped base,basew eb fillets at the junction of said base with said web and head-web fillets at the junction of said head with said web forming a 13 to 15 fishing angle,

lthe width4 of said headA being greater than its depth but not more than one and three-eighths times said depth and not more than four times the width of the web and less than one-half the width of the base which is less than the total height of the rail, the radii of said fillets being at least one-half the width of the web and the area of the circle inscribed in the head tangent to the web joining fillets and to the top of the head being at least '75% of the area of the head so the torsional constant of the head-web fillets is at least 25% greater than that, e. g., of a comparable A. R.. E. A. Standard T-raii of a given weight.

fillets and to thetop of the head, and a minimum web thickness of at least one-fourth the head width and not more than twice the radii of the head-web fillets to provide, as compared, e. g., with an vA. R. E, A. Standard T-'rail of approximately equal weight, a torsional constant (Kn) for the head 'of greater torsion-resisting capacity than that of said comparable T-r'ail;

13. A railway rail comprising a pentagonalshapedvhead, a web, a pentagonal-shaped base,

head-web filletsvat vthe junction of said head with said web and vbase-)web fillets at the junction of said base withvsaid web, said rail having a proportional distributionL of metal throughout characterized by having the-major portion of the area of its head within a circle inscribed in said head tangent to said head-web fillets and to the top of the rail, with the horizontal line of centroids of the head lying above the center of said circle,

a minimum web thickness of at least one-fourth the head width and not more than twice the radii of the head-webfillets, and a base width less than the total height of the rail but more than twice the widthof the head, to thereby locate the center of twist of` the rail in the thickened lower portion of the web below the point of compounding of the base-web fillets with the web, and to also provide torsional' constants 11. A railway rail comprising a pentagonalw forthe rail head and for the head-webfillets of greater torsion-resisting capacity than those, e. g.', of a Standard A. R. E. A. T-rail of approximately vequal weight.

. GEORGE R. BURKHARDT. 

